论文标题
离散时间Graphon的主方程平均野外游戏和团队
Master equation of discrete time graphon mean field games and teams
论文作者
论文摘要
在本文中，我们提出了一种等效的顺序分解算法，以计算GMFG的GMFE和Graphon Optimal Markovian策略（GOMPS）的Graphon平均场团队（GMFTS）（GMFTS）。我们考虑大量参与者依次做出战略决策，每个玩家的行动都会影响其邻居，该邻居在图形中捕获，该图形由已知的Graphon生成。每个玩家都会观察一个私人状态，也可以作为Graphon Mean-field人口状态，代表其他玩家类型的经验网络分布。我们考虑非平稳种群状态动力学，并提出一种新型的向后递归算法，以计算依赖两者的GMFE和GOMP，这两者都取决于玩家的私人类型以及通过Graphon确定的当前（动态）种群状态。计算GMFE的每个步骤均包括求解定点方程，而计算GOMP涉及解决优化问题。我们为存在这样的GMFE的模型参数提供条件。使用此算法，我们为不同图形的网络物理系统中的特定安全设置获得了GMFE和GOMP，以捕获系统中节点之间的相互作用。
In this paper, we present a sequential decomposition algorithm equivalent of Master equation to compute GMFE of GMFG and graphon optimal Markovian policies (GOMPs) of graphon mean field teams (GMFTs). We consider a large population of players sequentially making strategic decisions where the actions of each player affect their neighbors which is captured in a graph, generated by a known graphon. Each player observes a private state and also a common information as a graphon mean-field population state which represents the empirical networked distribution of other players' types. We consider non-stationary population state dynamics and present a novel backward recursive algorithm to compute both GMFE and GOMP that depend on both, a player's private type, and the current (dynamic) population state determined through the graphon. Each step in computing GMFE consists of solving a fixed-point equation, while computing GOMP involves solving for an optimization problem. We provide conditions on model parameters for which there exists such a GMFE. Using this algorithm, we obtain the GMFE and GOMP for a specific security setup in cyber physical systems for different graphons that capture the interactions between the nodes in the system.
